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I have an ordered response variable (stated preference from strong dislike to strong like) that is virtually uniformly distributed. I am using package ordinal in R to estimate the probability of an observation matrix X to fit into a specific ordered category Y. Christensen (2013, p18), in his explanation of the probit model, states that the observed response distribution should not deviate too much from a bell-shaped curve, else it ruins the quality of the estimates. Given that I have about as many observations in each category, my response clearly does not meet this criteria.

I'm not sure how to best deal with the data then. Any suggestion would be appreciated!

At the moment, when using a probit or logit model, my errors are almost perfectly normally distributed but only 1/3 observations gets assigned to the right group, which is a rather poor data fit. This might obviously mean that my predictors are just no good but I think the assumption of a normal response decreases the likelihood of correct predictions on the extremes, which gives my error distribution pretty fat tails.

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  • $\begingroup$ As far as I know, logit link within ordinal regression is used for a DV with any heavy-tailed distrubution, up to uniform. However, if your "uniform" distribution is clearly multimodal, cauchit link may be better. $\endgroup$ – ttnphns Jun 19 '14 at 14:54
  • $\begingroup$ Thanks for the feedback. I'm surprised you'd choose logit over probit as the latter has fatter tails than the logistic distribution. Regardless of the link, the log-likehood barely changes which must mean they are all (almost) equally bad/good. $\endgroup$ – SJDS Jun 19 '14 at 15:06
  • $\begingroup$ Why? Logistic tails are heavier than gaussian. $\endgroup$ – ttnphns Jun 19 '14 at 15:13
  • $\begingroup$ You're absolutely right. I misremebered. Cauchy seems to make a lot of sense then. Thanks!! $\endgroup$ – SJDS Jun 19 '14 at 15:26
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    $\begingroup$ Please note that we spoke of the distribution of the underlying continuous dependent variable, not the observed ordinal dependent variable. $\endgroup$ – ttnphns Jun 19 '14 at 20:42

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